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Quadratic equations GCSE revision guide
Revision guide outlining all you need to know about quadratic equations up to grade 5. Good for Foundation and Higher students. Suitable for Edexcel, AQA and OCR exam boards. Includes:
Expanding double brackets
Factorising quadratics
Difference of two squares
Solving quadratics by factorising
Sketching quadratic graphs without a table
Finding turning points of quadratic graphs (not by completing the square)
Using graphs to estimate solutions
Also get your higher quadratic equations revision guide following the link below.
https://www.tes.com/teaching-resource/higher-quadratics-gcse-revision-guide-12208545
Including:
Quadratic formula
Harder quadratics
Difference of two squares
Solving harder quadratic equations
Quadratic graphs
Quadratic inequalities
Transformations of quadratic graphs
Completing the square
Quadratic simultaneous equations
Click the link below to get more free revision guides. We won’t ask for your email or anything like that :)
https://flowmathematics.co.uk/revision-guides/
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Density
This well thought out worksheet has been structured to increase in difficulty gradually, beginning with scaffolded intro examples and building up to challenging extension questions that really get them thinking.
Under the hood
Calculating density
Calculating volume
Calculating mass
Calculations where the mass needs converting
Deciding if objects sink or float
Calculating the density when two liquids are mixed together
Thorough, comprehensive, and suitable for both KS3 and KS4. Our resources are carefully designed to boost confidence and grades.
Answers included
Not completely convinced? Download a free preview of the sheet here.
https://www.tes.com/teaching-resource/resource-12362987
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Calculating with rates
This well thought out worksheet has been structured to increase in difficulty gradually, beginning with scaffolded intro examples and building up to challenging extension questions that really get them thinking.
Under the hood
Rates not involving time
Rates involving time
Unitary method
Worded questions
Thorough, comprehensive, and suitable for both KS3 and KS4. Our resources are carefully designed to boost confidence and grades.
Answers included
Not completely convinced? Download a free preview of the sheet here.
https://www.tes.com/teaching-resource/resource-12361883
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Tree diagrams
This well thought out booklet has been structured to increase in difficulty gradually, beginning with scaffolded intro examples and building up to more challenging questions that get them thinking.
Under the hood
Intro examples completing an already drawn tree diagram
Using tree diagrams to calculate probabilities with replacement
Using tree diagrams to calculate probabilities without replacement
Drawing a tree diagram
Challenging examples involving finding probabilities of “at least one” success and tree diagrams with 3 branches/3 trials.
Thorough, comprehensive, and carefully designed to boost confidence and grades.
Answers included
Not completely convinced? Download a free preview of the sheet here.
https://www.tes.com/teaching-resource/resource-12482181
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Simultaneous equations - substitution
This well thought out worksheet has been structured to increase in difficulty gradually, beginning with scaffolded intro examples and building up to more challenging questions that get them thinking.
Under the hood
Simultaneous equations where one equation must be substituted into the other
Questions where one equation must be rearranged before substituting
Simultaneous equations which must be solved by putting them equal to one another
Thorough, comprehensive, and carefully designed to boost confidence and grades.
Answers included
Not completely convinced? Download a free preview of the sheet here.
https://www.tes.com/teaching-resource/resource-12420573
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Distance-time graphs
Free preview - This well thought out booklet has been structured to increase in difficulty gradually, beginning with scaffolded intro examples and building up to challenging extension questions that really get them thinking.
Under the hood
Calculating the speed by finding the gradient
Interpreting horizontal lines and downward sloping lines
Drawing a distance-time graph
Calculating average speed
Important: This is a free preview file. The full HQ sheet with answers included can be found here on TES by clicking the link below.
https://www.tes.com/teaching-resource/resource-12827146
Thorough, comprehensive, and suitable for both KS3 and KS4. Our resources are carefully designed to boost confidence and grades.
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Surds
Free preview - This well thought out worksheet has been structured to increase in difficulty gradually, beginning with scaffolded intro examples and building up to more challenging questions that get them thinking.
Under the hood
Simplifying surd expressions by multiplying and cancelling - e.g., √5 x √5 x √5 and 7/√7
Simplifying surds using the rule √ab = √a x √b
Expanding brackets that contain surds
Challenge questions involving surd expressions with fractions and writing expressions in the form p√q where q is the smallest possible integer
Important: This is a free preview file. The full HQ sheet with answers included can be found here on TES by clicking the link below.
https://www.tes.com/teaching-resource/resource-12830349
Thorough, comprehensive, and suitable for both KS3 and KS4. Our resources are carefully designed to boost confidence and grades.
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Transformations
This well thought out booklet has been structured to increase in difficulty gradually, beginning with scaffolded intro examples and building up to more challenging questions that get them thinking.
Under the hood
Reflecting shapes on a grid
Rotating shapes on a grid
Translating shapes on a grid
Describing reflections, rotations and translations
Challenge questions involving combined translations and reflecting in the lines y = x and y = -x.
Thorough, comprehensive, and carefully designed to boost confidence and grades.
Answers included
Not completely convinced? Download a free preview of the sheet here.
https://www.tes.com/teaching-resource/resource-12482174
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Decimals on the number line
This well thought out worksheet has been structured to increase in difficulty gradually, beginning with scaffolded intro examples and building up to challenging extension questions that really get them thinking.
Under the hood
One decimal place number lines
Two decimal place number lines
Three decimal place number lines
Four decimal place number lines
Thorough, comprehensive, and suitable for both KS3 and KS4. Our resources are carefully designed to boost confidence and grades.
Answers included
Not completely convinced? Download a free preview of the sheet here.
https://www.tes.com/teaching-resource/resource-12362479
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Enlargement - Area and volume
This well thought out booklet has been structured to increase in difficulty gradually, beginning with scaffolded intro examples and building up to challenging extension questions that really get them thinking.
Under the hood
Enlargement using the area scale factor
Enlargement using the volume scale factor
Finding missing lengths when given the areas (or volumes) of similar shapes
Harder questions that involve combining volume and surface area
Thorough, comprehensive, and carefully designed to boost confidence and grades.
Answers included
Not completely convinced? Download a free preview of the sheet here.
https://www.tes.com/teaching-resource/resource-12363431
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Enlargement on a grid
This well thought out worksheet has been structured to increase in difficulty gradually, beginning with scaffolded intro examples and building up to challenging extension questions that really get them thinking.
Under the hood
Enlarging shapes on a grid with horizontal and vertical sides
Enlarging shapes on a grid that have diagonal sides
“Enlarging” shapes on a grid when the scale factor is a fraction
Describing enlargements on a grid. I.e., scale factor, centre of enlargement
Thorough, comprehensive, and suitable for both KS3 and KS4. Our resources are carefully designed to boost confidence and grades.
Answers included
Not completely convinced? Download a free preview of the sheet here.
https://www.tes.com/teaching-resource/resource-12363449
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Velocity-time graphs
This well thought out booklet has been structured to increase in difficulty gradually, beginning with scaffolded intro examples and building up to more challenging questions that get them thinking.
Under the hood
Interpreting constant acceleration velocity-time graphs - i.e., using gradient to find the acceleration, finding the distance by calculating the area underneath
Estimating the acceleration from a curved velocity-time graph
Calculating the average acceleration between two points
Using trapeziums to estimate the distance from a curved velocity-time graph
Thorough, comprehensive, and carefully designed to boost confidence and grades.
Answers included
Not completely convinced? Download a free preview of the sheet here.
https://www.tes.com/teaching-resource/resource-12482195
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Quadratic inequalities
This well thought out worksheet has been structured to increase in difficulty gradually, beginning with scaffolded intro examples and building up to more challenging questions that get them thinking.
Under the hood
Solving quadratic inequalities
Solving quadratic inequalities that need rearranging first
Challenge questions that involve forming quadratic inequalities and listing integer solutions that satisfy pairs of inequalities
Thorough, comprehensive, and carefully designed to boost confidence and grades.
Answers included
Not completely convinced? Download a free preview of the sheet here.
https://www.tes.com/teaching-resource/resource-12409684
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Probability and equations (Algebraic probability)
A well thought out worksheet of very challenging questions that combine probability, ratio and algebra to stretch those students aiming for grades 8 and 9.
Includes conditional probability examples and those where a quadratic equation must be derived.
Thorough, comprehensive, and carefully designed to boost confidence and grades.
Answers included.
Not completely convinced? Download a free preview of the sheet here.
https://www.tes.com/teaching-resource/resource-12395470
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Area of a trapezium
This well thought out worksheet has been structured to increase in difficulty gradually, beginning with scaffolded intro examples and building up to challenging extension questions that really get them thinking.
Under the hood
Applying the formula
Examples with slanted sides that must be ignored.
Trapeziums that have been rotated.
Trapeziums that don’t look like the standard one the students are used to.
Working backwards from the area to find missing lengths.
Thorough, comprehensive, and suitable for both KS3 and KS4. Our resources are carefully designed to boost confidence and grades.
Answers included.
Not completely convinced? Download a free preview of the sheet here.
https://www.tes.com/teaching-resource/resource-12361829
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Expanding double brackets
This well thought out worksheet has been structured to increase in difficulty gradually, beginning with scaffolded intro examples and building up to challenging extension questions that really get them thinking.
Under the hood
Examples with positive numbers inside the brackets
Examples with negative numbers inside the brackets
Examples with numbers in front of x inside the brackets - e.g., (2x + 3)(5x - 4)
Examples with more than one different letter in the brackets - e.g., (x + 3)(y + 4)
Examples where the bracket is squared - e.g., (x - 3)^2
Thorough, comprehensive, and carefully designed to boost confidence and grades.
Answers included
Not completely convinced? Download a free preview of the sheet here.
https://www.tes.com/teaching-resource/resource-12361421
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Estimating powers and roots
This well thought out worksheet has been structured to increase in difficulty gradually, beginning with scaffolded intro examples and building up to challenging extension questions that really get them thinking.
Under the hood
Estimating square roots - i.e., finding the pairs of whole numbers they sit between
Estimating powers of numbers by rounding them to one significant figure
Thorough, comprehensive, and carefully designed to boost confidence and grades.
Answers included
Not completely convinced? Download a free preview of the sheet here.
https://www.tes.com/teaching-resource/resource-12364181
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Circle theorems
This well thought out booklet has been structured to increase in difficulty gradually, beginning with scaffolded intro examples and building up to challenging extension questions that really get them thinking.
Under the hood
Angle at the centre double that at the circumference
Angles in semicircles
Angles in the same segment
Angles in cyclic quadrilaterals
Angles where tangents meet radii or where two tangents meet
Alternate segment theorem
Exam style questions where a combination of the theorems must be applied
Thorough, comprehensive, and carefully designed to boost confidence and grades.
Answers included
Not completely convinced? Download a free preview of the sheet here.
https://www.tes.com/teaching-resource/resource-12361934
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Completing the square
This well thought out worksheet has been structured to increase in difficulty gradually, beginning with scaffolded intro examples and building up to challenging extension questions that really get them thinking.
Under the hood
Completing the square when the coefficient of x^2 is 1
Completing the square when the coefficient of x^2 is not 1
Completing the square when the coefficient of x is odd (number inside brackets will be a fraction)
Finding turning points of graphs
Thorough, comprehensive, and carefully designed to boost confidence and grades.
Answers included
Not completely convinced? Download a free preview of the sheet here.
https://www.tes.com/teaching-resource/resource-12361955
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Areas of compound shapes
This well thought out worksheet has been structured to increase in difficulty gradually, beginning with scaffolded intro examples and building up to challenging extension questions that really get them thinking.
Under the hood
Intro examples where missing lengths don’t need to be found
Harder examples where missing lengths do need to be found
Examples where one of the simple shapes is a triangle
Examples where pieces have been cut from rectangles
Thorough, comprehensive, and suitable for both KS3 and KS4. Our resources are carefully designed to boost confidence and grades.
Answers included
Not completely convinced? Download a free preview of the sheet here.
https://www.tes.com/teaching-resource/resource-12361843